the shopkeeper sold a laptop having its cost price rupees 25000 at a profit of 25% find its selling price ​

Answer:

6

Step-by-step explanation:

you can find the mean by adding up all of the numbers, and then dividing that total by the amount of numbers in the sequence.

Julia have to pay $2.57 as sales tax on purchase of headphones.

Given,

The cost of headphones which Julia wants to purchase on sale = $ 42.79

The sales tax in Julia's country = 6%

We have to calculate the amount of sales tax Julia will pay on the purchase:

That is,

Sales Tax Value = Percentage of sales tax × Price of headphones

Sales Tax Value = (6 / 100) × 42.79

Sales Tax Value = 0.06 × 42.79

Sales Tax Value = 2.5674

Sales Tax Value ≈ 2.57

Therefore, Julia have to pay $2.57 as sales tax on purchase of headphones.

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Approximately 31.7 people signed up for both yoga and aerobics.

What is probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

Let's define the following events:

Event A: a person signed up for yoga.

Event B: a person signed up for aerobics.

P(A) = 92/756

P(B) = 113/756

P(neither A nor B) = 575/756

We can use the following formula:

P(A and B) = P(A) + P(B) - P(A or B)

We can calculate P(A or B) as:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 92/756 + 113/756 - P(A and B)

P(A or B) = 205/756 - P(A and B)

P(neither A nor B) = 1 - P(A or B)

Substituting in the calculated value for P(A or B), we get:

575/756 = 1 - (205/756 - P(A and B))

575/756 = 551/756 + P(A and B)

P(A and B) = 24/756

P(A and B) ≈ 0.0317

Therefore, approximately 31.7 people signed up for both yoga and aerobics.

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As y increases by 1, y increases by 1 then we have found that function rule has a greater slope.

To determine this, we find the slope of the graph

The slope of the 3 graphs can be calculated by applying the slope equation to any two selected points.

Consider that use the points (0,2) and (-1,0)

We have it as:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = (0 -2)/(-1 - 0)

m = 2

Now, for the function, we have the slope as 3 then the slope is change in y divided by the change in x.

We can conclude that 3 is greater than 2, and as such the slope of the function is greater.

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Answer:

C, or D

Step-by-step explanation:

The answer is C, or D

Answer:

8 x + 14

Step-by-step explanation:

2(4x+7)

2×4x +2×7 =

8x+14

With the help of permutation and combination we conclude that the correct matches are:

Ordered selections with repetition: [choose]

Ordered selection without repetition: [choose]

Unordered selection without repetition: [choose]

Unordered selection with repetition: [choose]

What is permutation?

In mathematics and combinatorics, a permutation refers to an arrangement or ordering of objects. It is a way of selecting and arranging a set of items in a specific order.

Here's how the selection types correspond to the number of ways the selection can happen:

Ordered selections with repetition: [choose]

In this selection type, the order of selection matters, and repetition is allowed. This means that an object can be selected multiple times. The number of ways to make the selection is denoted by \(n^k\), where n represents the number of available objects and k represents the number of objects to be selected.

Ordered selection without repetition: [choose]

In this selection type, the order of selection matters, but repetition is not allowed. Each object can be selected only once. The number of ways to make the selection is denoted by P(n, k), which represents the number of permutations of k objects chosen from n distinct objects. The formula for P(n, k) is n! / (n - k)!

Unordered selection without repetition: [choose]

In this selection type, the order of selection does not matter, and repetition is not allowed. Each object can be selected only once. The number of ways to make the selection is denoted by C(n, k) or n choose k, which represents the number of combinations of k objects chosen from n distinct objects. The formula for C(n, k) is n! / (k! * (n - k)!).

Unordered selection with repetition: [choose]

In this selection type, the order of selection does not matter, and repetition is allowed. Each object can be selected multiple times. The number of ways to make the selection is denoted by C(n + k - 1, k) or (n + k - 1) choose k, which represents the number of combinations of k objects chosen from n distinct objects when repetition is allowed. The formula for C(n + k - 1, k) is (n + k - 1)! / (k! * (n - 1)!).

So, the correct matches are:

Ordered selections with repetition: [choose]

Ordered selection without repetition: [choose]

Unordered selection without repetition: [choose]

Unordered selection with repetition: [choose]

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The statement "The results of the experiment do not agree with the theory, there's something wrong with the experiment" is wrong as it does not indulge any other reasons for the results of the experiment not agreeing with the theory.

This statement assumes that the experiment is always at fault and neglects the possibility that the theory may be incorrect or incomplete.

The outcome of an experiment can be influenced by various factors, such as measurement errors, incorrect experimental design, or limitations of the equipment used.

Thus, it is always important to consider multiple explanations before concluding that there is a problem with the experiment.

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Step-by-step explanation:

Hey there!

The given equation is;

y = 3x - 2

Make table for"X" and "y"

x = 0 1 2

x = -2 1 4

Now;

The coordinates are; (0,-2) , (1,1), (2,4).

After that plot them on graph.

Hope it helps...

In a poll conducted by a certain research​ center, 1046 adults were called after their telephone numbers were randomly generated by a​ computer, and were able to correctly identify the random sampling.

Each sample has an equal chance of being chosen as part of the sampling technique known as random sampling. A randomly selected sample is intended to be a fair representation of the entire population.

In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a procedure for randomly choosing a sample.

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The given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3.

What is the linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The equation 4x=3y-7

So, here we can solve this equation for the x as well as y equals,

Firstly we will solve for x:

4x = 3y - 7

dividing the whole equation by 4 we get,

4x/4 = (3y - 7)/4

x = (3y - 7)/4

Similarly, we will solve for y:

4x = 3y - 7

3y = 4x + 7

dividing the whole equation by 3 we get,

3y/3 = (4x + 7)/3

y = (4x + 7)/3

Hence, the given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3

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Answer:

The slope of the line would be 3/4

Step-by-step explanation:

When you put the coordinates in the point-slope formula, it would be 4 - (-2) over 7 - (-1). The answer would then be 6/8 but if simplified, the answer would then be 3/4.

If the diagonal of the quadrilateral bisect each other at a right angle. Then the quadrilateral will be a rhombus.

It is a polygon with four sides. The total interior angle is 360 degrees. A rhombus's opposite sides are parallel and equal.

The diagonal of the rhombus will intersect at a right angle.

From the diagram, the diagonal of the rhombus will intersect at a right angle.

That means the diagonals bisect each other.

Thus, if the diagonal of the quadrilateral bisect each other at a right angle. Then the quadrilateral will be a rhombus.

The diagram is given below.

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The transfer function T(s) = (s² + 3s + 7)(s + 1)(s² + 5s + 4) can be represented in a block diagram as a combination of summing junctions, integrators, and transfer functions.

In the given transfer function T(s) = (s² + 3s + 7)(s + 1)(s² + 5s + 4), we have three distinct factors in the numerator and three distinct factors in the denominator. Each factor represents a specific component in the block diagram.

The first factor (s² + 3s + 7) corresponds to a second-order transfer function with natural frequency and damping factor. This can be represented by a block with two integrators in series and a summing junction.

The second factor (s + 1) represents a first-order transfer function, which can be depicted as an integrator.

The third factor (s² + 5s + 4) represents another second-order transfer function with natural frequency and damping factor.

By combining these individual components in the block diagram, we can obtain the overall representation of the transfer function.

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Answer:

c is the answer

Step-by-step explanation:

Answer:

We need the following three rigid motions:

i) Reflection around y-axis, ii) Translation three units in the -y direction, iii) Translation four units in the -x direction.

Step-by-step explanation:

We need to perform three operations on pentagon ABCDE to create pentagon A'B'C'D'E':

i) Reflection around y-axis:

\((x',y') = (-x,y)\) (Eq. 1)

ii) Translation three units in the -y direction:

\((x'',y'') = (x', y'-3)\) (Eq. 2)

iii) Translation four units in the -x direction:

\((x''',y''') = (x''-4, y'')\) (Eq. 3)

We proceed to proof the effectiveness of operations defined above by testing point D:

1) \(D(x,y) = (-1, 4)\) Given.

2) \((x',y') = (1,4)\) By (Eq. 1)

3) \((x'',y'') = (1, 1)\) By (Eq. 2)

4) \(D'(x,y) = (-3,1)\) By (Eq. 3)/Result

When a pregnant woman drinks alcohol, it can seriously damage the development of the fetal nervous system. This is because alcohol can cross the placenta and enter the fetal bloodstream, interfering with the growth and function of the brain and other organs.

The most severe form of alcohol-related fetal damage is fetal alcohol syndrome (FAS), which can lead to physical, cognitive, and behavioral problems that can last a lifetime.

Alcohol consumption during pregnancy can have serious and lasting effects on the developing fetus. The nervous system is particularly vulnerable, as alcohol can interfere with the growth and function of the brain and other organs. Fetal alcohol syndrome (FAS) is the most severe form of alcohol-related damage and can cause physical, cognitive, and behavioral problems that can last a lifetime. It is crucial for pregnant women to avoid alcohol altogether to protect the health and well-being of their unborn child.

In conclusion, drinking alcohol during pregnancy can cause serious harm to the fetal nervous system and lead to lasting developmental problems. It is essential for pregnant women to avoid alcohol entirely to protect the health and well-being of their baby.

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Answer:

Answer = -0.5, -2/5, 0, 0.67, 7/9

Step-by-step explanation:

negative to positive

Answer:

-2/5,-0.5,0,0.6,7/9

Answer:

a = 6

Step-by-step explanation:

Given

\(\frac{a}{3}\) + 4 = 6 ( subtract 4 from both sides )

\(\frac{a}{3}\) = 2 ( multiply both sides by 3 to clear the fraction )

a = 6

Answer:

a=6

Step-by-step explanation:

a/3=6-4

a/3=2

a=6

The construction correctly finds the best location of the warehouse is shown in option C (Construction Y because point E is the circumcentre of triangle LMN and due to its exact equidistant location from the three stores at L, M, and N, Point E is the ideal location for the warehouse.)

The location that is equally spaced from the three vertices and where the perpendicular bisectors of a triangle's sides intersect.

Calculation for distance of the three stores from warehouse:

Precisely one circle crosses through all three, which are all on the same line. Finding the centre of the circle that goes through all three of the points is equivalent to finding the point that is equally distant from each of the three points (since all points on a circle are equidistant from the centre).

L, M, and N are our points. To create the triangle, draw the lines LM, LN, and MN. The junction of any two of the lines' perpendicular bisectors, point E, will serve as the circle's centre.

Due to the fact that E is the triangle's LMN's circumcenter, as demonstrated in Construction Y.

Therefore, given that it is precisely equidistant between the three stores at L, M, and N, this is the optimal location for the warehouse.

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Answer:

the answer is C.

Step-by-step explanation:

construction X, because point E is the circumcenter of angle LMN.

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Mid point of any two points (x1,y1) and (x2,y2)

is ((x1+x2)/2,(y1+y2)/2)

using this

we get coordinates of d are (a,-2b)

The limit, if it exists for lim t =  \(6t - 6t^2 = 6t(1 - t)\) is 6. Therefore, the limit exists and is equal to 6.

The denominator is approaching 0; the limit does not exist and is equal to infinity (i.e., "dne"). To evaluate the limit as t approaches 0, we can try simplifying the expression first by factoring out a t from the numerator:

\(6t - 6t^2 = 6t(1 - t)\)

We can simplify the expression by factoring out 6t from the numerator:

6t - 6t^2

= 6t(1 - t)

So the expression becomes:

lim t→0 6t - 6t^2 t

= lim t→0 6(1 - t)

Now we can directly substitute t=0 into the expression since the limit is approaching 0:

lim t→0 6(1 - t)

= 6(1 - 0)

= 6

Therefore, the limit exists and is equal to 6.

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Work Shown:

r = 6 = radius

V = volume of a sphere of radius r

V = (4/3)*pi*r^3

V = (4/3)*pi*6^3

V = 904.77868423386

V = 904.8

I used my calculator's stored version of pi (instead of something like pi = 3.14)

The units "cubic meters" can be abbreviated to m^3 or \(m^3\)

The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.

         The volume of a sphere can be calculated using the formula:

V = \(4/3 * \pi * r^3\),

Where V is the volume and r is the radius of the sphere.

\(\pi\) = 3.14

The radius of the sphere (r) = 6m

Plugging in the given radius of 6m into the formula, we get:

V = (4/3) * \(\pi\) * (6^3)

V = 1.333 * \(\pi\) * 216

V = 1.333 * 3.14 * 216

V = 4.1866 * 216

V = 904.8 cubic meters

Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8  cubic meters.

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The volume of the grain is the combination of the hemisphere and cylinder. Then the volume of grain is 19460.57 cubic feet.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The volume of the shape is the combination of the hemisphere and cylinder.

Volume of grain = volume of a hemisphere + volume of a cylinder

The volume of a hemisphere will be

\(\rm Hemisphere \ volume = \dfrac{2}{3}\pi r^3\\\\\\Hemisphere \ volume = \dfrac{2}{3}\pi 6^3\\\\\\Hemisphere \ volume = 452.57\)

The volume of a cylinder will be

\(\rm Cylinder \ volume = \pi r^2 h\\\\\\Cylinder \ volume = \pi *6^2 * 168\\\\\\Cylinder \ volume = 19008\)

The volume of the shape will be

Volume of grain = 19008 + 452.57

Volume of grain = 19460.57

The volume of grain is 19460.57 cubic feet.

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The values of constants are b = -6 and c = 8

The values of x are log base 4 of 3 or log base 4 of 5

Given equation,

(4^x-1) ²- 6(4^x-1) + 8 = 0

Let this equation be f(x) i.e., f(x) = (4^x-1) ²- 6(4^x-1) + 8 (equation 1)

In question it's mentioned that y = 4^x-1

Now substitute this 'y' value in equation 1. We get,

f(y) = y ²- 6y + 8 (Here, f(x) changed to f(y) because the equation now is in terms of y)

It's in form of y² + by + c = 0 where b = -6 and c = 8

Factorizing f(y),

y ²- 6y + 8 = 0

y ²- 4y -2y + 8 = 0 (Since, -6 = -4 -2)

y(y - 4) -2(y - 4) = 0

(y - 2)(y - 4) = 0

So, y = 2 or 4

i.e., 4^x-1 = 2 or 4

if 4^x-1 = 2 then

4^x-1 = 2

4^x = 3

x = log base 4 of 3

else (i.e., 4^x-1 = 4)

4^x-1 = 4

4^x = 5

x = log base 4 of 5

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Answer:

38

Step-by-step explanation:

If the level of GDP increased by $400 billion in a private closed economy with a marginal propensity to consume of 0.80, aggregate expenditures must have increased by $400 billion.

If the level of GDP increased by $400 billion in a private closed economy where the marginal propensity to consume (MPC) is 0.80, we can calculate the increase in aggregate expenditures.

The marginal propensity to consume (MPC) represents the proportion of additional income that people choose to spend. In this case, with an MPC of 0.80, it means that for every additional dollar of income, people will spend $0.80 and save $0.20.

To calculate the increase in aggregate expenditures, we can use the concept of the expenditure multiplier, which is the inverse of the marginal propensity to save (MPS). The MPS is equal to 1 - MPC.

MPS = 1 - MPC

MPS = 1 - 0.80

MPS = 0.20

The expenditure multiplier (k) is calculated as:

k = 1 / MPS

k = 1 / 0.20

k = 5

Now, we can calculate the increase in aggregate expenditures (ΔAE) using the formula:

ΔAE = ΔGDP × k

ΔAE = $400 billion × 5

ΔAE = $2000 billion

Therefore, the correct answer is $2000 billion.

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Answer:

52.948 m²

Step-by-step explanation:

→ State the formula for the area

length × width

→ Substitute in the numbers

8.68 × 6.1 = 52.948 m²